1. Recently, your college surveyed 100 students across campus and found that the mean age of students taking calculus is 23. (Suppose the standard deviation is 2.01 years.) (a) Explain why we can assume that the distribution is approximately normal. We can assume that the distribution of ages of students taking calculus is approximately normal because of the central limit theorem. According to the central limit theorem, if we have a sample size large enough in this case, 100 students and the population distribution is not extremely skewed then the sampling distribution of the mean will be approximately normal. In this case, we have a sample of 100 students which is considered large enough. Additionally, we have no reason to believe that the population distribution of ages is extremely skewed so we can assume that the distribution of ages in the population is approximately normal as well. Therefore, we can conclude that the distribution. Of ages of student's taking calculus is approximately normal. (b) What are the mean and standard deviation for the sample mean ages of calculus students? The mean of the sample mean ages of calculus students would be the same as a mean age of the population, which is given as 23. The standard deviation of the sample mean ages of calculus students also known as the standard error of the mean can be calculated using the formula standard error of the mean = standard deviation divided by the square root of the sample size. (2) Find the 90th percentile for the mean age of calculus students. Round to 1 decimal place. The Z score corresponding to the 90% out is approximately 1.28. Upper Limit= mean + Z score X standard error of the mean substituting to get them values we get: Upper Limit= 23 + 1.28 0,201 = 23.257 (d) Find the probability that a calculus student is younger than 18. Substituting to getting values we get: 2.01/100= 0,201, therefore the mean of the sample mean ages of calculus students is 23 and a standard deviation of the sample mean ages is 0,201. Therefore the 90th percentile of the main age of 23.3 years rounded to 1 decimal place. (e) Is it unusual for a calculus student to be a minor? Explain your answer.